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Lý thuyết Phương trình quy về phương trình bậc hai - SGK Toán 10 Kết nối tri thức

A. Lý thuyết 1. Phương trình dạng \(\sqrt {a{x^2} + bx + c} = \sqrt {d{x^2} + ex + f} \)

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A. Lý thuyết

1. Phương trình dạng \(\sqrt {a{x^2} + bx + c}  = \sqrt {d{x^2} + ex + f} \)

Để giải phương trình \(\sqrt {a{x^2} + bx + c}  = \sqrt {d{x^2} + ex + f} \), ta thực hiện như sau: - Bình phương hai vế và giải phương trình nhận được. - Thứ lại các giá trị x tìm được ở trên có thỏa mãn phương trình đã cho không và kết luận nghiệm.

2. Phương trình dạng \(\sqrt {a{x^2} + bx + c}  = dx + e\)

Để giải phương trình \(\sqrt {a{x^2} + bx + c}  = dx + e\), ta thực hiện như sau: - Bình phương hai vế và giải phương trình nhận được. - Thứ lại các giá trị x tìm được ở trên có thỏa mãn phương trình đã cho không và kết luận nghiệm.


B. Bài tập

Bài 1: 🐻Giải phương trình \(\sqrt {2{x^2} - 4x - 2}  = \sqrt {{x^2} - x - 2} \).

Giải:

Bình phương hai vế của phương trình, ta được \(2{x^2} - 4 - 2 = {x^2} - x - 2\).Sau khi thu gọn, ta được \({x^2} - 3x = 0\). Từ đó tìm được x = 0 hoặc x = 3.Thay lần lượt hai giá trị này của x vào phương trình đã cho, ta chỉ thấy có x = 3 thỏa mãn.Vậy nghiệm của phương trình đã cho là x = 3.

Bài 2: 🔜Giải phương trình \(\sqrt {2{x^2} - 5x - 9}  = x - 1\).

Giải:

Bình phương hai vế của phương trình, ta được \(2{x^2} - 5x - 9 = {x^2} - 2x + 1\).Sau khi thu gọn, ta được \({x^2} - 3x - 10 = 0\). Từ đó tìm được x = -2 hoặc x = 5.Thay lần lượt hai giá trị này của x vào phương trình đã cho, ta chỉ thấy có x = 5 thỏa mãn.Vậy nghiệm của phương trình đã cho là x = 5.

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